Antenna utilizing intermediate cuspate reflector to couple energy from feed to main reflector



March 15, 1966 s. P. MORGAN ANTENNA UTILIZING INTERMEDIATE CUSPATEREFLEGTOR T0 COUPLE ENERGY FROM FEED TO MAIN REFLECTOR 196s Filed Dec.16,

N GP* /A/l/EA/TOA S. MORGAN 7' TORA/EV March 15, 1966 s. P. MORGANANTENNA UTILIZING INTERMEDIATE CUSPATE REFLECTOR TO COUPLE ENERGY FROMFEED TO MAIN REFLECTOR 2 Sheets-Sheet 2 Filed Deo. 16, 1963 v .MSK

United States Patent O ANTENNA UTILIZING INTERMEDIATE CUSPATE REFLECTORT COUPLE ENERGY FROM FEED TO MAIN REFLECTOR Samuel P. Morgan,Morristown, NJ., assignor to Bell Telephone Laboratories, Incorporated,New York, N.Y., a corporation of New York Filed Dec. 16, 1963, Ser. No.330,701

18 Claims. (Cl. 343-781) This invention relates to antenna systems, andmore particularly, to improvements in Cassegrainian and Gregorianantenna systems.

Recently antennas employing Cassegrainian .and Gregorian telescopeprinciples have been found to be very useful in radio communicationsystems. yEach antenna, taking the name of the optical telescope afterwhich it is patterned, has a main, concave paraboloidal reflector with afeed element at its vertex and a smaller, intermediate reflector locatedin front of the main reflector to couple radio waves between the mainreflector and the feed element. The Cassegrainian .antenna employs anintermediate reflector having a convex surface, usually hyperboloidal,situated between the main reflector and its focus, and theGregorianantenna employs an intermediate reflector having a concave surface,usually ellipsoidal, so situated that the focus of the main reflectorlies between the main and intermediate reflectors. Among the advantagesof Cassegrainian and Gregorian an-tenna arrangements i-s the eliminationof the transmission line found necessary in conventionalfeed-at-the-focus paraboloidal antennas to interconnect the terminalequipment to the feed element.

A problem in the design of Cassegrainian and Gregorian antennas(visualizing the antenna as transmitting) is reflection back into thefeed element of energy that is radi-ated from the feed element and thatis reflected from the intermediate reflector and intended fortransmission to the main reflector. This phenomenon, hereafter calledback reflection, has the effect of creating an impedance mismatch forenergy coupled Ibetween the feed element and the reflectors when theantenna is receiving as well as when it is tr-ansmitting. Although animpedance mismatch can quite easily be elimina-ted for waves of a singlefrequency or a narrow band of frequencies, it is not possible toeliminate impedance mismatch over a broadband of frequencies. As aresult the transmission characteristics between the feed element and thereflectors are frequency dependent outside of avery restricted band offrequencies.

Back reflection has been avoided in one prior art antenna .arrangementby mounting a small cone on the surface of the intermediate reflector to.scatter the energy that would otherwise be reflected back into thefeed. A scattering cone has several adverse effects on the electricalcharacteristics of an antenna system. First, it may unduly increase thewide-angle side lobes of the antenna radiation pattern. Wide-angle `sidelobes are particularly undesirable in receiving applications where it isimportant that the antenna be insensitive to noise coming fromdirections far removed from the direction of the main beam. Second, thescattered energy is not utilized and therefore the potential gain of theantenna system is not fully realized. This second effect is especiallypronounced in antennas in which the feed element is a so-called nearfield feed, disclosed in a patent application of D. C. Hogg, Serial No.143,078, filed October 5,1961, and .assigned to the assignee of thisinvention. In this case, the feed aperture is very large so thepotential lback reflection is large and the cone scatters an inordinateamount of energy.

It is therefore the obje-ct of this invention to avoid back reflectionin a Cassegrainian or Gregorian antenna system .3,24l,l47 Patented Mar.15, 1966 ICC without adversely affecting the antennas electricalcharacteristics.

In accordance with the above object an antenna system is providedhavin-g -a large, concave main reflector, a feed element located nearthe main reflector, and a small intermediate reflector having a cuspatereflecting surface, the intermediate reflector coupling waves Ibetweenthe feed element and the main reflector. As employed in thisspecification, the term cuspate surface is a surface that projects twocurved lines meeting at an apex onto at least one plane intersecting thesurface. The cuspate shape of the intermediate reflector permitscoupling between it and the main reflector of a wave having -a hole inits wave front. The hole is so situated and is of such size that theinside boundary of the wave front irradiated from the cuspate reflectorcircumscribes the effective feed aperture when the Wave front isimpinging upon the main reflector. The effective feed -aperture is takento mean the area ofthe feed element over which waves impinging upon thefeed element are received by it, regardless of whether the feed element-actually has a physical aperture through which waves are received. As aresult, no back reflection into the feed element takes place and nomeasures to correct impedance mismatch are necessary. The shape of thesurface of the main reflector is appropriately deformed from theconvention-al parabolic shape so that antenna system accommodates planeWaves at the aperture of the main reflector.

The intermediate reflector can take the shape of the inside surface of acusp having concave sides, the outside surface of a cusp having concavesides, `the inside surface of a cusp having convex sides, or the outsidesurface of a cusp having convex sides, depending upon the manner inwhich energy is coupled between the feed element and the main reflector.

These and other features of the .invention will become more apparentfrom consideration of the following detailed description taken inconjunction with the drawings in which FIGS. 1 through 4 show antennaarrangements according to the invention, each having a different type ofcuspate intermediate reflector. For ease of visualization the antennaarrangements shown in lFIGS. 1 through 4 will be described in terms oftheir use as transmitting antennas. They function in a reciprocalfashion in reception of electromagnetic waves and are equallyadvantageous for this purpose.

FIG. l discloses a Cassegrainian antenna comprising a feed element 6, anintermediate reflector 10, and a main reflector 8 whose surfaces can bedefined in terms of a cylindrical coordinate system having an axialcoordinate designated z, a radial coordinate designated r, and an angle0 that a plane passing through the z axis and the point to be definedmakes with the plane of the drawing. It is assumed that the intermediatereflectors and the main reflectors of all the embodiments exhibitrotational symmetry around an axis, represented by the z axis, in FIG.l. Thus, the surfaces of reectors 8 and 10 are formed by rotating thecurves representing reflectors 8 and 10 about the z axis and thecoordinate angle 0 can be disregarded because the coordinate r and zvalues of a surface are the same for all. values of 0. Thus, the usualway of forming the reflectors of a directional antenna system results ina radiation pattern for the antenna system which is directional in anyplane passing through the z axis. Feed element 6 is of the so-callednear field type disclosed in the above-mentioned D. C. Hogg application.It is a conventional horn-reflector that accommodates waves having aplane wave front and that has an opening so designed that intermediatereflector 10 lies in its near eld. mission, electromagnetic wavesemanating from terminal equipment block 2 are coupled to feed element 6by' 3 means of a wave guide section 4. Feed element 6 directs the wavesin a plane wave front toward inter mediate reflector 10.

The path of electromagnetic energy between feed element 6 and the fareld of the antenna is illustrated by means of a ray diagram. For thepurpose of the following qualitative explanation of the mode ofoperation and the later quantitative analysis, it is assumed that thebehavior of electromagnetic waves can be explained in terms of geometricoptics, because the effects of diffraction on the antennacharacteristics the invention seeks to improve are small. The center ofthe wave emanating from feed element 6, represented by ray A, afterimpinging upon intermediate reflector 10, divides into segments B andB', which impinge upon main reflector 8 at the inside extremity of itsgeometrically illuminated surface. After reflection from main reflector8, resulting rays C and C' are radiated into the antenna far field. RaysD andY D', showing the boundaries of the wave radiated from feed element6, impinge upon the geometrically illuminated extremity of intermediatereflector 10 and are reflected therefrom as rays E and E'. Rays E and Eilluminate main reflector 8 at the outside extremity of itsgeometrically illuminated surface and are reflected therefrom into thefar field of the antenna as rays F and F. Translation of the ray diagraminto three dimensional terms indicates that intermediate reflector 10,having the shape of the outside surface of a convex cusp, transforms theplane wave front that emanates from feed element 6, having a circularsurface, into a curved wave front, having a ring-shaped surface theinside and outside circumferences of which expand as the wave `frontprogresses from intermediate reflector 10 to main reflector 8. By thetime that the curved wave front has reached main reflector 8, the insidecircumference of its surface has expanded to such a size that itcircumscribes the effective aperture of feed element 6. As a result,substantially no energy emanating from feed element 6 is reflected backinto it. All the energy is used to illuminate main reflector 8, and thuscontributes to the antenna system gain. Main reflector 8 iscorrespondingly deformed from the conventional paraboloidal shape toeffect transformation of the curved wave front impinging upon it into anemergent plane wave front.

The remaining embodiments of the invention, shown in FIGS. 2 through 4,differ from the arrangement in FIG. 1 only in the shape of theintermediate and main reflectors. In considering the modes of operationof these arrangements, the same letters are used to identifycorresponding rays in the ray diagrams in order to facilitatecomparis-on of the ray paths of the various embodiments.

FIG. 2 discloses a Gregorian antenna comprising a main reflector 12 andan intermediate reflector 14 having the shape of the inside surface of aconvex cusp. In this arrangement, unlike the Cassegrainian antenna ofFIG. 1, rays emanating from feed element 6 are reflected from one sideof intermediate reflector 14 to the opposite side of main reflector 12.Thus, rays D and D' reflect lfrom the geometrically illuminatedextremity of intermediate reflector 14 as rays E and E', which crosseach other. As explained in connection with FIG. 1, cuspate intermediatereflector 14 transforms the plane wave `front having a circular surfacethat emanates from feed element 6 into a curved wave front having aring-shaped surface whose inside circumference circumscribes theeffective aperture of feed element 6.

In FIG. 3 an antenna arrangement is shown comprising a main reflector 16and an intermediate reflector 18 having the shape of the inside surfaceof a concave cusp. This arrangement can be considered to be a crossedCassegrainian antenna because the rays impinging upon one side of thesurface of intermediate reflector 18 from feed element 6 impinge uponthe other side of the surface of main reflector 16. Also, rays E and E',reflected yfrom the geometrically illuminated extremity of intermediatereflector 18, impinge upon the geometrically illuminated inside edge ofmain reflector 16. If the two reflectors are chosen to have practicalproportions, it may easily occur that intermediate reflector 18 blockssome energy impinging upon it for transmission to main reflector 16.This drawback can be seen in FIG. 3 by tracing the path of ray A, whichought to reflect from intermediate reflector 18 as shown by dashed linesB, C, B', and- C', but which is prevented from so doing by the shape ofintermediate reflector 18. As a result, illumination of main reflector16 may be somewhat inefficient and the gain of the antenna system maythus be smaller than in the other arrangements.

In FIG. 4 an antenna arrangement is shown compr1s ing a main reflector2f) and an intermediate reflector 22 having the shape of the outsidesurface of a concave cusp. This arrangement can be considered to be anuncrossed Gregorian antenna because the rays impmgmg upon one side ofthe surface of intermediate reflector 22 from feed element 6 impingeupon the same side of the surface of main reflector 20. Rays E and E',reflected from the geometrically illuminated extremity of intermediatereflector 22, impinge upon the geometrically 1lluminated inside edge ofmain reflector 20, and rays B and B', reflected from the apex ofintermediate reflector 22, impinge upon the geometrically illuminatedoutside edge of main reflector 20. l

Equations will now be developed which define the in-j termedatereflector and main reflector shapes requiredV to satisfy the raydiagrams shown in the drawings. For the purpose of this analysis, it isassumed -that geometnc optics describes the electromagnetic fieldestablished between feed element 6 and the aperture of the mainreflector and that a wave having a plane wave front across the apertureof the main reflector is desired. In this analysis terms are defined asfollows:

r1 is a variable defining the r coordinate of the intermedi! atereflector; n

Z1 is a variable defining the z coordinate of the intermediatereflector;

r2 is a variable defining the r coordinate of the main reflector;

z2 is a variable defining the z coordinate of the main reflector;

c1 is a constant representing the z coordinate of the apex of theintermediate reflector;

b1 is a constant representing the r coordinate of the geometricallyilluminated extremity of the intermediate reflector surface alsocoinciding with the r coordinate of the edge of the aperture of feedelement 6;

dl is a constant representing the z coordinate of the geometricallyilluminated extremity of the intermediate reflector surface;

a2 is a constant representing the r coordinate of the geo-r metricallyilluminated inside edge of the main reflector surface;

b2 is a constant representing the r coordinate of the geo# metricallyilluminated outside edge of the main reflector surface; and

d2 is a constant representing the z coordinate of the geometricallyilluminated outside edge of the main reflector surface.

Reference is now made to FIG. 1, in order to formulate the equationsdefining the reflectors shown therein. Because every ray path from feedelement 6 to an arbitrarily chosen plane lying perpendicular td the Zaxis must be the same in order to produce a plane, Wave front across theaperture of the main reflector,

C=C1+(fl22+C12)`/ (2) The power flow per unit area at the intermediatereflector, S1(r1), depends upon the radiation pattern of feed element 6and the power flow per unit area at the main reflector, S2(r2), ischosen to produce the radiation pattern specified for the antennasystem. The physical law of conservation of power makes possibleformulation of the relationship between r1 and r2.

where S1 and S2 have been normalized relative to one another so thatInspection of the ray diagram of FIG. 1 indicates that tan 2 =tr ZF Z2(5) where p is the angle of incidence andreection of a typical ray ateach reflector (go is measured relative to a line normal to thereliector in question). By solving Equation 1 for zf-z2, substitutingthe expression for z1iz2 into Equation 5, and employing thetrigonometric identity between the tangent of an angle and the tangentof its double angle, one obtains where dl'g Integrating Equations 7results in 1 r 21(7'1) :C1-2li@ @L 1T2 (P1) dpi 2.. 2 r2 T2 2O@ -f-l/.zcada 8 where the relationship between r1 and r2 is given by Equation 3and C is defined by Equation 2. Thus, given the antenna dimensions c1,b1, a2, and b2, the power flow at the intermediate reflector 81(11), andthe power flow at the main reliector S2(r2), Equations 2, 3, and 8permit computations of the surfaces of the intermediate reflector andmain reflector 8. If a2 is made equal to zero and if S1 and S2 are madeconstant independent of position, Equations 8 reduce to the equationsdefining the conventional near-lield Cassegrainian antenna, Le., aparaboloidal main rellector confocal with a paraboloidal intermediatereflector. It is the specilication of a2 to be nonzero that accounts forthe development of the cusp in the intermediate reflector and it is thespecification of. a2 to be at least as large as the radius of theeffective aperture of the feed element that accounts for elimination ofback reection altogether.

Frequently applications call for a constant power flow at the reflectorsurfaces. In this case,

According to Equations l0 the intermediate' reflector ought to exhibit aminute area of concavity very near the apex of the cusp. This inflectionin the equations can be ignored in the construction of physicalembodiments of intermediate reflector 10 because the concavity onlyaffects the geometrically determined power ow after reflection fromintermediate reliector 10 at the inside boundary of the wave front,where the elfects of diffraction predominate in any event.

By a parallel analysis, the surfaces of main reflector 12 andintermediate reliector 14 of the Gregorian antenna shown in FIG. 2 canbe expressed as where Equation 3 gives the relationship between r1 andr2 and C is defined by Equation 2. In the special case of uniform powerflow at the reliector surfaces, Equations 1l reduce to (l2) l Z2=lfz2ll22) +S21/272 7`22'*a22)1/2 S21/2,122 cosh-1 112 Using a parallelanalysis for the so-called crossed Cassegraiuian arrangement of FIG. 3the shapes of main reflector 16 and intermediate reflector 18 aredetermined to be C=d1+[(b1+2)2+d12]/ (14) and the relationship betweenr1 and r2 is given by L Smpapldwfm :smaad/12 15 In the special case ofuniform power liow at the reflectors, Equations 13 reduce to whichdelines the shapes of main reflector 20 and intermediate reflector 22where and Equation defines the relationship between r1 and r2. Uniformpower flow at the reflector surfaces of this arrangement causesEquations 17 to reduce to Both the main reflector and the intermediatereflector shown in FIGS. 1, 2, and 4 are extended in area beyond thegeometrically illuminated surface to reduce spillover, which in practiceoccurs due to diffraction. Most conveniently the shapes of thereflectors shown in FIGS. 1 and 2 can be extended in accordance with theequations defining their shapes within the geometrically illuminatedregion. As the equations defining the shapes of the reflectors of FIG. 4do not produce real solutions outside of the geometrically illuminatedregion the shapes of these reflectors can conveniently be extended byextrapolation. The shape of the main reflector between the geometricallyilluminated inside edge, a2, and the opening of feed element 6 can beany convenient shape.

It is possible to practice the invention using intermediate and mainreflectors which have other than rotationally symmetric shapes,depending upon the type of antenna radiation pattern that is desired.For example, main and intermediate reflectors having a cylindrical shapemight be employed if a radiation pattern having a directionalcharacteristic in only one plane is desired. Such a reflector is formedby translating lcurves similar to those representing the reflectors inthe drawings along an axis perpendicular to the plane `of the drawings.The precise reflector shapes are found by an Ianalysis parallel to theanalysis employed for reflectors having rotational symmetry.

Although the invention provides a large improvement whn used with a nearfield feed, as described, the conventional horn feed element thataccommodates waves having spherical wave fronts can also be employed. Inthis case, the intermediate reflectors remain cuspate, but the newequations exactly dening the intermediate and main reflector surfacesmust be derived by means of an analysis parallel to that employed abovein the cases of a feed element accommodating waves having plane wavefronts.

What is claimed is:

1, An antenna system accommodating electromagnetic waves ofpredetermined wavelength and having a plane wave front and comprising aconcave reflector and cuspate reflector situated on a common axis, saidcupsate reflector facing the concave surface of said concave reflector,and -a feed element situated near the intersection of said axis and saidconcave reflector, said feed element having an aperture facing towardsaid cuspate reflector and accommodating electromagnetic waves having aplane wave front, said aperture having a diameter of at least several`of said wavelengths, and said cupsate reflector having a diameter atleast as large as the aperture of said feed element, said cuspatereflector thereby serving to couple electromagnetic waves `between saidfeed element and said concave reflector.

2. The antenna system of claim l in which said cuspate reflector has theshape of the outside surface of a convex cusp.

3. The antenna system of claim 1 in which said cuspate reflector has theshape of the inside surface of a convex cusp.

4. The antenna system of claim 1 in which said Icuspate reflector hasthe shape of the inside surface of a `concave cusp.

5. The antenna system of claim 1 in which said cuspate reflector has theshape of the outside surface of a concave cusp.

6. An antenna system accommodating electromagnetic waves ofpredetermined wavelength and having a plane wave front and comprising amain reflector situated on an axis, a feed element situated near theintersection of said axis and said main reflector, said feed elementhaving an aperture facing away from said main reflector along said axisand accommodating electromagnetic waves having a plane wave front, saidaperture having a diameter of at least several of said wavelengths, andan intermediate reflector situated on said axis and facing thereflective surface of said main reflector, said intermediate reflectorhaving a cuspate surface with a diameter at least as large as thediameter of the aperture of said feed element such that when the antennasystem is transmitting the inside circumference of the area of the wavefront traveling from said intermediate reflector to said main reflectorcircumscribes the effective aperture of said feed element when said wavefront illuminates said main reflector.

7. The antenna system of claim 6 in which said intermediate reflectorhas the shape of the outside surface of a convex cusp.

8. The antenna system of claim 6 in which said intermediate reflectorhas the shape of the inside surface of a convex cusp.

9. The antenna system of claim 6 in which said intermediate reflectorhas the shape of the inside surface of a concave cusp.

10. The antenna system of claim 6 in which said intermediate reflectorhas the shape of the outside surface of a COIlCaVe CllSp.

lll. An antenna system comprising a concave reflector situated on anaxis, a smaller cuspate reflector situated on said axis and facing theconcave surface of said concave reflector, and a feed element situatednear the intersection of said axis and said concave reflector, said feedelement facing toward said cuspate reflector and said cuspate reflectorserving to couple electromagnetic Iwaves between said feed element andsaid concave reflector, in which said reflectors are situated onmutually perpendicular r and z axes, said feed element accommodateselectromagnetic waves having plane wave fronts, and said reflectors areshaped with rotational symmetry around the z axis such that they projecton the plane of the r and z axes curves defined by Z1 is a variabledefining the z coordinate of said cuspate reflector,

r1 is a variable defining the r coordinate of said cuspate reflector,

Z2 is a variable defining the z coordinate of said concave reflector,

r2 is a variable defining the r coordinate of said concave reflector,

c1 is a constant representing the z coordinate of the apex of saidcuspate reflector,

a2 is a constant representing the r coordinate of the geometricallyilluminated inside edge of said concave reflector,

S1(p1) is the function expressing power flow per unit area at saidcuspate reflector, and

9 S2022) is the function expressing power flow per unit area at saidconcave reflector, a2 being larger than one-half of the diameter of theeffective aperture of said feed element.

12. An antenna system comprising a concave reflector situated on anaxis, a smaller .cuspate reflector situated on said axis and facing theconcave surface of said concave reflector, and a feed element situatednear the intersection of said axis and said concave reflector, said feedelement facing toward said cuspate reflector and said cuspate reflector`serving to couple electromagnetic waves between said feed element andsaid concave reflector, in which `said reflectors are situated onmutually perpendicular r and z axes, said feed element accommodateselectromagnetic waves having plane wave fronts, and said reflectors areshaped ywith rotational symmetry around the z axis such that theyproject on the plane of the r and z axes curves defined by Z1 is avariable defining the z coordinate of said cuspate reflector,

r1 is a variable defining the r coordinate of said cuspate reflector,

z2 is a variable defining the z coordinate of said concave reflector,

r2 is a variable defining the r coordinate of said concave reflector,

c1 is a constant representing the z coordinate of the apex of saidcuspate reflector,

a2 is a constant representing the r coordinate of the geo metricallyilluminated inside edge of said concave reflector,

S1(p1) is the function expressing power flow per unit area at saidcuspate reflector, and

S2022) is the function expressing flow per unit area at said concavereflector, a2 being larger than one-half the diameter of the effectiveaperture of said feed element.

13. An antenna system comprising a concave reflector situated on anaxis, a smaller cuspate reflector situated on said axis and facing theconcave surface of said concave reflector, and a feed element situatednear the intersection of said axis and said concave reflector, said feedelement facing toward said cuspate reflector and said cuspate reflectorserving to couple electromagnetic waves between said feed element andsaid concave reflector, in which said reflectors yare situated onmutually perpendicular r and z axes, said feed element accommodateselectromagnetic waves having plane wave fronts, and said reflectors areshaped with rotational symmetry around the z axis such that they projecton the plane of the r and z axes curves defined by zl is a variabledefining the z coordinate of said cuspate reflector,

r1 is a variable defining the r coordinate of said cuspate reflector,

z2 is a variable defining the z coordinate of said concave reflector,

r2 is a variable defining the r coordinate of said concave reflector,

b1 is a constant representing the r coordinate of the geometricallyilluminated extremity of said cuspate rellector,

d1 is `a constant representing the z coordinate of the geometricallyilluminated extremity of said cuspate reflector,

a2 is a constant representing the r coordinate of the geometricallyilluminated inside edge of said concave reflector,

S1(p1) is the function expressing power flow per unit area at saidcuspate reflector, and

S2(p2) is the function expressing power flow per unit area at saidconcave reflector, a2 being larger than one-half the diameter of theeffective aperture of said feed element.

14. An antenna system comprising a concave reflector situated on anaxis, a smaller cuspate reflector situated on said axis and facing theconcave surface of said concave reflector, and a feed element situatednear the intersection of said axis and said concave reflector, said feedelement facing toward said cuspate reflector and said cuspate reflectorserving to couple electromagnetic waves between said feed element andsaid concave reflector, in which said reflectors are situated onmutually perpendicular r and z axes, `said feed element accommodateselectromagnetic waves having plane wave fronts, and said reflectors areshaped with rotational symmetry around the z axis such that they projecton the plane of the r and z axes curves ldefined by Z1 is a variabledefining the z coordinate of said cuspate reflector,

r1 is a variable defining the r coordinate of Said cuspate reflector,

r2 is a variable defining the z coordinate of said concave reflector,

b1 is a constant representing the r coordinate of the geometricallyilluminated extremity of said cuspate reflector,

d1 is a constant representing the z coordinate of the geometricallyilluminated extremity of said cuspate reflector,

a2 is a -constant representing the r coordinate of the geometricallyilluminated inside edge of said concave reflector,

S1(p1) is the function expressing power flow per unit area at saidcuspate reflector, and

S2(p2) is the function expressing power flow per unit` area at saidconcave reflector, a2 being larger than one-half the diameter of theeffective aperture of said feed element.

15. An antenna system comprising a main reflector situated on an axis, afeed element situated near the intersection of said axis and said mainreflector, said feed element facing away from said main reflector andpointing along said axis, and an intermediate reflector situated on saidaxis and facing the rellectivesurface of said main reflector, saidintermediate reflector having a cuspate surface such that when theantenna system is transmitting the inside circumference of the area ofthe wave front traveling from said intermediate reflector to said mainreflector circumscribes the effective aperture of said feed elementlwhen it illuminates said main reflector, in which said reflectors aresituated on mutually perpendicular r and z axes, said feed elementaccommodates electromagnetic waves having plane wave fronts, and saidreflectors are shaped with rotational symmetry around the z axis suchthat they project on the plane of the r and z axes curves defined bywhere Z1 is a variable defining the z coordinate of said intermediatereflector,

ri is a variable defining the r coordinate of said intermediatereflector,

z2 is a variable defining the z coordinate of said main reflector,

r2 is a variable defining the r coordinate of said main reflector,

c1 is a constant representing the z coordinate of the apex of saidintermediate reflector,

b1 is a constant representing ther coordinate of the geometricallyilluminated extremity of said intermediate reflector,

a2 is a constant representing the r coordinate of the geometricallyilluminated inside edge of said main reflector, and

b2 is a constant representing the r coordinate of the geometricallyilluminated edge of said main reflector, a2 being larger than one-halfthe diameter of the effective aperture of said feed element and thepower flow per unit area at said intermediate reflector being constant.

16. An antenna system comprising a main reflector situated on an axis, afeed element situated near the intersection of said axis and said mainreflector, said feed element facing away from said main reflector andpointing along said axis, and an intermediate reflector situated on saidaxis and facing the reflective surface of said main reflector, saidintermediate reflector having a cuspate surface such that when theantenna system is transmitting the inside circumference of the area ofthe wave front traveling from said intermediate reflector to said mainreflector circumscribes the effective aperture of said feed element whenit illuminates said main reflector, in which said reflectors aresituated on mutually perpendicular r and z axes, said feed elementaccommodates electromagnetic waves having plane wave fronts. and saidreflectors are shaped with rotational symmetry around the three axessuch that they project on the plane of the r and z axes curves definedby where 0:01 l (M24-C12) 1/2 blz Z1 is a variable defining the zcoordinate of said intermediate reflector,

rl is a variable defining the r coordinate of said intermediatereflector,

z2 is a variable defining the z coordinate of said main reflector,

r2 is a variable defining the r coordinate of said main reflector,

c1 is a constant representing the z coordinate of the apex of saidintermediate reflector,

b1 is a constant representing the r coordinate of the geometricallyilluminated extremity of said intermediate reflector,

a2 is a constant representing the r coordinate of the geometricallyilluminated inside edge of said main reflector, and

b2 is a constant representing the r coordinate of the geometricallyilluminated outside edge 0f said main reflector, a2 being larger thanone-half the diameter of the effective aperture of `said feed elementand the power flow per unit area at said intermediate reflector beingconstant.

17. An antenna system comprising a main reflector situated on an axis, afeed element situated near the intersection of said axis and said mainreflector, said feed element facing away from said main reflector andpointing along said axis, and an intermediate reflector situated on saidaxis and facing the reflective surface of said main reflector, saidintermediate reflector having a cuspate surf-ace such that when theantenna system is transmitting the inside circumference of the area ofthe wave front traveling from said intermediate reflector to said mainreflector circumscribes the effective aperture of said feed element whenit illuminates said main reflector, in which said reflectors aresituated on mutually perpendicular r and z axes, said feed elementaccommodates electromagnetic waves having plane wave fronts, and saidreflectors are shaped with rotational symmetry around the z axis suchthat they project on the plane of the r and z axes curves defined by Z1is a variable defining the z coordinate of said intermediate reflector,r1 is a variable defining the r coordinate of said intermediatereflector, z2 is a variable defining the z coordinate of said mainreflector, r2 is a variable defining the r coordinate of said mainreflector,

b1 is a constant representing the r coordinate of the geometricallyilluminated extremity of said intermediate reflector,

d1 is a constant representing the z coordinate of the geometricallyilluminated extremity of said intermediate reflector,

a2 is a `constant representing the r coordinate of the geometricallyilluminated inside edge of said main reflector, and

b2 is a constant representing the r coordinate of the geometricallyilluminated outside edge of said main reflector, a2 being larger thanone-half the diameter of the effective aperture of said feed element andthe power flow per unit area at said intermediate reflector `beingconstant.

18. An antenna system comprising a main reector situated on an axis, afeed element situated near the intersection of said axis and said mainreflector, said feed element facing away from said main reflector andpointing along saidaxis, and an intermediate reflector situated on saidaxis and facing the reflective surface of said main reflector, saidintermediate reflector having a cuspate surface such that when theantenna system is transmitting the inside circumference of the area ofthe wave front traveling from said intermediate reflector to said mainreflector circumscribes the effective aperture of said feed element whenit illuminates said main reflector, in which said reflectors aresituated on mutually perpendicular r and z axes, said feed elementaccommodates electromagnetic waves having plane wave fronts, and saidreflectors are shaped with rotational symmetry around the z `axis suchthat they project on the plane of the r and z axes curves defined by zlis a variable defining the z coordinate of said intermediate reflector,1'1 is a variable defining the r coordinate of said intermediatereflector, z2 is a variable defining the z coordinate of said mainreflector, r2 is a Variable defining the r coordinate of said mainreflector, b1 is a constant representing the r coordinate of thegeometrically illuminated extremity of said intermediate reflector, d1is a const-ant representing the z coordinate of the geometricallyilluminated extremity of said intermediate reflector, a2 is a constantrepresenting the r coordinate of the geometrically illuminated insideedge of said main reflector, and b2 is a constant representing the rcoordinate of the geometrically illuminated outside edge of said mainreflector, a2 being larger than one-half the diameter of the effectiveaperture of said feed element and the power flow per unit area at saidintermediate reflector being constant.

References Cited by the Examiner UNITED STATES PATENTS 2,477,694 8/1949Gutton 343--837 HERMAN KARL SAALBACH, Primary Examiner.

1. AN ANTENNA SYSTEM ACCOMMODATING ELECTROMAGNETIC WAVES OFPREDETERMINED WAVELENGTH AND HAVING A PLANE WAVE FRONT AND COMPRISING ACONCAVE REFLECTOR AND CUSPATE REFLECTOR SITUATED ON A COMMON AXIS, SAIDCUPSATE REFLECTOR FACING THE CONCAVE SURFACE OF SAID CONCAVE REFLECTOR,AND A FEED ELEMENT SITUATED NEAR THE INTERSECTION OF SAID AXIS AND SAIDCONCAVE REFLECTOR, SAID FEED ELEMENT HAVING AN APERTURE FACING TOWARDSAID CUSPATE REFLECTOR AND ACCOMMODATING ELECTROMAGNETIC WAVES HAVING APLANE WAVE FRONT, SAID APERTURE HAVING A DIAMETER OF AT LEAST SEVERAL OFSAID WAVELENGTHS, AND SAID CUSPATE REFLECTOR HAVING A DIAMETER AT LEASTAS LARGE AS THE APERTURE OF SAID FEED ELEMENT, SAID CUSPATE REFLECTORTHEREBY SERVING TO COUPLE ELECTROMAGNETIC WAVES BETWEEN SAID FEEDELEMENT AND SAID CONCAVE REFLECTOR.